Question

For each of the following variables, state the scale of measurement that each variable appears to represent, and make sure to provide a brief rationale for your decision.

The primary language of an individual’s grandmother

IQ scores

Reading comprehension ability of eighth-grade students, as demonstrated by their percentile rank performance (relative to a national norm) in a standardized reading comprehension test.

House numbers

The system of military grades for those enlisted in the U.S. Navy

Answer 1

The primary language of an individual’s grandmother - Nominal

IQ scores

[Interval] An IQ score (or a standardized score on many other kinds of tests, such as achievement tests) is probably best considered as falling at an interval level of measurement. Some argue that such scores are at the ordinal level, providing only an ordering of performance. But, given the large number of potential values (95% of the population falls between 70 and 130 on an IQ scale), the scores function well as interval-scaled values.

Reading comprehension ability of eighth-grade students, as demonstrated by their percentile rank performance (relative to a national norm) in a standardized reading comprehension test.

- Ordinal

House numbers - Ordinal

Here, the sequence of numbers is meaningful, but not the distance between them. Consider house numbers on a street. If you live at number 2 on your street, and your friend Jane lives at number 12, and Fred is at number 22 when you leave your house you will pass Jane's house before reaching Fred's, but the distance from you to Jane, and from Jane to Fred is not necessarily the same. So, you can say that Fred lives further than Jane, but you can only get a crude estimate of how much further from the house numbers because the houses may be different in size (unless, that is, you are in England, where there are whole streets of identical houses).   Thus it is not really legitimate to add and subtract numbers in an ordinal scale. Another example is if you ask a patient to rate their pain on a 0 to 10 scale. We cannot really claim that an increase from 2 to 5 on the scale is the same change as a shift from 5 to 8. We don't know if the person is really using the pain scale in a truly linear manner.